What are specific examples that show that the children are not paying attention to Atticus’ advice about their actions toward other people?

In Chapter 9, Atticus tells Scout that he'll be defending
Tom Robinson and explains that people might say bad things about him in her
presence:

You might hear some ugly talk about it at school,
but do one thing for me if you will: you just hold your head high and keep those fists
down.  No matter what anybody says to you, don't you let 'em get your goat.  Try
fighting with your head for a change...it's a good one, even if it does resist
learning.

Later in the chapter, when the family visits
Finch's landing, Scout "forgets" Atticus's advice.  When her cousin, Francis, taunts her
with regard to Atticus's defense of Tom Robinson, she attacks him and splits her
knuckles on his teeth. 

As clairewait notes, Atticus's
attack on Walter Cunningham is another example of Scout's impulsivity.  Because Atticus
knows his daughter's short temper, and because he knows that the citizens of Maycomb say
very ugly things in certain situations (like the one he's entering into with Tom
Robinson), he continually advises Scout to control herself.  As she is young and
passionate about what she perceives is right and wrong, though, it's sometimes hard for
her to control herself.